I will try and describe two Prince Valiant scenarios that mark the distinction I'm drawing, both found in the Episode Book.
The Crimson Bull, by Jerry Grayson, unfolds over multiple events in place as the PCs lead the bull of the title to the Vale of Mud. But these are really just extended framing - they don't presuppose particular prior decisions by the players other than to lead the bull to the Vale; and they provide colour and enrich the situation concerning the bull. The actual moment of crunch is in the finale, when the players (as their PCs) have to decide what to do with the bull and the pagan sacrifice of it by the wise woman of the Vale. I think it's a really well-conceived scenario.
A Prodigal Son - in Chains, by Mark Rein-Hagen, has some interesting elements but, as presented, is a railroad in the sense I've tried to set out above. The tell-tale in the writing is stuff like this:
At this point the Adventurers’ actions can have a direct impact on the story. They can meet with the yeomen leaders of the peasant army, try to sneak into the castle, run to get help from nearby nobles, or attack or harass the peasant army. Bryce does what they ask, but strongly requests that they let him speak with the peasant army.
Whatever happened, you need to have things end up with Bryce’s father, the duke, dead. . . .
Just as things seem to be winding down (one way or another) Bryce steps out of the crowd . . .
At this point you need to have things wind up with someone trying to kill someone else as a result of the heated argument over what to do. It can be a peasant trying to kill a yeoman, Alia trying to kill Samson, Samson trying to kill an Adventurer; but no matter what happens, Bryce throws himself in the way . . .
In other words, there are moments of choice that are thematically weighty (how do the PCs deal with the politics and associated dynamics between the "prodigal son", his father the duke and his sister Alia) which have to come out a certain way for the scenario to play out as presented. When I used the scenario I picked up some of the key story elements but just ignored all of Rein-Hagen's sequencing and railroading.
I've gone into this level of detail because I think we have to look very closely at the details of how situations and events are being presented, how they relate to thematic framing and resolution, etc, before we can start to identify whether or not we're looking at a railroad.
Also, I think what Jerry Grayson has done is not only better as RPG design (at least relative to my preferences) but displays more ingenuity as a RPG writer. I think it takes a lot of cleverness to set out an extended framing that builds up the pressure in the overarching situation but without forcing resolutions on the way through that then force railroading if the whole scenario is to be used. I can think of a few other published scenarios that pull this off - at least some of Robin Laws's in the Hero Wars Narrator's Book; and as a site-based version, some of those in a 3E-era d20 supplement called Wonders Out of Time (I can't remember the publisher).